Analysis options

# Analysis options

## Mass redistribution

Last updated: Jan 08, 2024 11:15:20

The mass redistribution procedure is implemented. For time history analysis and each spectrum dynamic load case, a set of mass redistribution groups may be defined. It is possible to comply with the building code's requirements thanks to this technology, which includes taking into account the torsional effects of unknown mass locations and spatial variations in earthquake loads.

Every group has the following parameters:

• Position of the local coordinate system of the group. There are two options to define the position of this coordinate system: default and specifying the angle of rotation about the global Z-axis.
• Mass relocation along the local axis R` (Eak_R`).
• Mass relocation along the local axis T` (Eak_T`).
• A list of items to create a group.

Groups of mass redistribution in elements

The default position of the UCS for the group is determined in the following way:

• for single-component earthquake loads - the direction of the local X-axis is determined as the projection of the earthquake load on the XOY-plane of the global coordinate system;
• for three-component earthquake loads with radial components - the direction of the local X-axis coincides with the direction of the radial component of the earthquake load;
• for other spectral dynamic loads and time history analysis - the local coordinate system of the group coincides with the global coordinate system.

The purpose of mass redistribution is to move the centres of masses by the specified displacements, Eak_R` and Eak_T`.

Important.

The group redistributes masses obtained from loads and mass weights applied to the elements and directly to the internal nodes of the group. The internal nodes of the group are the nodes that belong only to the elements of the group. To collect the masses from the FE into the nodes of this element, a diagonal mass matrix is used, no matter what type of matrix has been specified.

## Damping ratio

Last updated: Jan 08, 2024 11:15:20
• For dynamic modules 41 and 64, calculation of damping ratios by mode shapes (according to damping ratios specified for elements).

Note: In LIRA-SAPR 2022 R2, in analysis on accelerograms of earthquake load with dynamic modules 27 and 29 for design models consisting of elements or fragments with different damping properties, the analysis of equivalent attenuation by the j-th eigenmode of vibrations was implemented by the following formula:

ξj={φj}T*∑[ξK]i*{φj}/{φj}T*[K]*{φj}

where {φj} is the vector of the j-th mode shape, [K] is the stiffness matrix of the model, ∑[ξK]i is the stiffness matrix (for the i-th element or fragment) multiplied by the damping ratio for this element.

• New option to use separately the damping ratios for each dynamic load case in the dynamic modules 27/29 and 41/64. For these modules, it is possible to limit the damping ratio: for 27 and 29 - maximum damping ratio, for 41 and 64 - minimum and maximum Nu.

Account of damping in the spectral method

## Seismic isolators

Last updated: Jan 08, 2024 11:15:20

For friction FEs 263/264, the "Unloading with initial stiffness" option is implemented. With this option, you can apply the hysteresis behaviour of FE in the cyclic loading: the friction load T=N*mf, where mf is the friction coefficient defined in the stiffness parameters, activates when the direction of motion changes (i.e., when the velocity equals 0). In "unloading with initial stiffness", the FE of friction enables you to describe, for example, the behaviour of a friction seismic isolator and, in combined behaviour with the FE of an elastic spring, a friction pendulum seismic isolator.

Friction pendulum seismic isolator

## Pushover Analysis

Last updated: Jan 08, 2024 11:15:20
• For Pushover Analysis, new option to set the user-defined steps for application of horizontal earthquake load and to take into account the damping ratio.

• For Pushover Analysis, it is possible to use iterative FEs; previously, only step-type FEs were used. This option, for instance, enables the use of nonlinear hinges and inelastic springs to account for the local plasticity.

Example. FE of inelastic springs in Pushover Analysis

## Finite element "Joint"

Last updated: Jan 08, 2024 11:15:20

The option "Unloading with initial stiffness" is added for the FE of joint. Unloading is performed by an elastic-plastic model with initial stiffness from the point of the current state. Re-loading is performed along the path of the previous unloading, so the joint will return to the point with the maximum strain that was achieved earlier. The relationship between the vertical stiffness and the shear stiffness for the FE of joint is shown in the figure below.

Behaviour of the FE of joint during unloading (vertical and shear stiffness)

## Tools for evaluating properties and analysis results

Last updated: March 26, 2024
• For problems with time history analysis, there is a new option to display mosaic plots of accelerations and velocities for all nodes of the model in the global or local coordinate system. It is also possible to view animation of acceleration and velocity changes in time.

Mosaic plots of acceleration and velocity for all nodes of the model for problems with time history analysis
• For problems with time history analysis, the diagram of response spectrum is generated in the directions X, Y, Z, UX, UY, UZ on the basis of calculated accelerations for the certain node of the model.

Diagrams of change in displacement, acceleration as a function of time. Diagram of nodal response spectrum
• For a node with a specified accelerogram, there is a new option to generate acceleration and response spectrum graphs as the sum of the specified graph and the graph obtained from the analysis results.

• New option to select the presentation of mosaic plots for initial, final and relative values of nonlinear stiffnesses of plates and bars calculated as a result of the "NL Engineering 1" (iterative method for characteristic load case) and physically nonlinear analysis that simulates erection process ("Assemblage", "NL Engineering 2" (stepwise method for characteristic load case), "Progressive Collapse"). Mosaic plots of calculated final stiffnesses are added for 1-node and 2-node finite elements that simulate elastic springs with account of ultimate force (FE 251, 252, 255, 256, 261, 262, 265, 266) and nonlinear elastic springs (FE 295, 296).

Initial, final and relative values of the bending stiffness of plates along the unified local X1-axes
• For physically nonlinear problems with iterative solids, there are options to view, evaluate and prepare documentation for the calculated parameters of the stress-strain state. In the "Section (state)" window, the following analysis results for the certain iterative solid are presented:

• mosaic plot of normal stress in the main material /reinforcement of the solid;
• mosaic plot of nominal strain in the main material /reinforcement of the solid;
• mosaic plot of tangential stress τxy/ τxz/ τyz in the main material of the solid;
• mosaic plot of nominal strain γxy/ γxz/ γyz in the main material of the solid.

Evaluation of the stress state of the main material and reinforcement in a physically nonlinear iterative solid
• New modes for mosaic plots are implemented to evaluate the soil pressure:

• Mosaic plot of soil pressure Rz (per r.m.) (N/m);
• Mosaic plot of soil pressure Ry (per r.m.) (N/m);
• Mosaic plot of soil pressure Rz/Bc (N/m^2);
• Mosaic plot of soil pressure Ry/Hc (N/m^2).

Note.

Bc - width of settlement zone, dimension parallel to the Y1-axis of the bar (m);
Hc - width of settlement zone, dimension parallel to the Z1-axis of the bar (m)

## New types of perfectly rigid body (PRB)

Last updated: Jan 08, 2024 11:15:20

New types of PRBs are implemented.

Now, PRB may be one of the following types:

• All degrees of freedom (DOF)
• X, Y, Z, UX, UY, UZ
• Z, UX, UY
• Y, UX, UZ
• X, UY, UZ
• X, Y, UZ
• X, Z, UY
• Y, Z, UX
• X, Y, UX, UY, UZ
• X, Z, UX, UY, UZ
• Y, Z, UX, UY, UZ

Directions for the degrees of freedom(DOF) correspond to the directions of the local coordinate system of the master node.

The PRB was limited to type 1 ("All degrees of freedom") earlier. This meant that the slave and master nodes were connected by the identical values for warping (model type 6) and temperature (model type 15), in addition to the kinematic restraints between X, Y, Z, UX, UY, and UZ.

The 2nd type of PRB imposes only kinematic restraints between X, Y, Z, UX, UY, and UZ.

PRB of types 3-5 connect the displacements of the slave and master nodes as they move out of the certain planes. As a result, the displacements of the slave and master nodes are independent in this plane.

PRB of types 6-8 connect the displacements of the slave and master nodes in the certain plane. As a result, the displacements of the slave and master nodes are independent when they move out of the certain plane.

PRB of types 9-11 make the displacements of the slave and master nodes independent only along the appropriate axis.

Now, a node can serve as the master for multiple PRBs simultaneously.

Let’s consider modelling a slab-wall intersection, where the slab "leaves a trace" in the shape of a PRB in the wall and the wall "leaves a trace" in the shape of a PRB in the slab.

Example. How to use the PRB

Previously, the model in the figure was modelled by three PRBs:

1, 4, 5, 48, 51

2, 6, 7, 47, 50

3, 8, 9, 46, 49

Now this can be modelled with the six PRBs. This will release the degrees of freedom in the PRB in directions that do not require restraint. For example, so that the slab and wall nodes in the PRB can move freely from thermal heating.

1, 4, 5 (PRB type 3. Z, UX, UY)

1, 48, 51 (PRB type 5. X, UY, UZ)

2, 6, 7 (PRB type 3. Z, UX, UY)

2, 47, 50 (PRB type 5. X, UY, UZ)

3, 8, 9 (PRB type 3. Z, UX, UY)

3, 46, 49 (PRB type 5. X, UY, UZ)

That is, 1, 4, 5 is an unbending body in the XOY-plane, but can deform in that plane,

and 1, 48, 51 is an unbending body in the YOZ plane, but can deform in that plane.

Important.

When you open the problems generated in previous versions, all PRBs are of type 1 (all degrees of freedom).

A slave node can be part of only one PRB and a slave node cannot be a master node.

## Analysis options

Last updated: March 26, 2024
• Dynamics module (32) was updated in accordance with the requirements of "SNRA 20.04-2020. Building code, the Republic of Armenia. Design of structures for earthquake resistance. General rules".

How to define parameters for the earthquake load according to SNRA 20.04-2020 (Armenia)
• For iterative solids, information about the stress-strain state of the cross-section is added to evaluate the state of the main material and reinforcement.

• For nonlinear elastic springs (FE 295, 296), the final stiffnesses are calculated.

## Nonlinear behaviour of soil

Last updated: Jan 08, 2024 11:15:20
• Account of the max soil resistance for the nonlinear behaviour of elastic base for bars and plates.

Previously, the nonlinear behaviour of the elastic base for bars and plates meant only that C1/C2 was ignored in uplifting (one-sided behaviour). Now, in addition to the one-way behaviour, it is also possible to define an max soil resistance in compression. That is, now there are two variants of behaviour for the elastic base:

• one-way behaviour and no limitation on max resistance of soil;
• one-way behaviour and limitation on the max compressive resistance of the soil.
• New option to get the max design resistance from the calculation in the SOIL system.

Important.

The max resistance of soil should be a negative value. If no data are available or the value is greater than or equal to zero, it is considered that the max soil resistance is not specified.

Nonlinear behaviour of the soil in compression

## New type of force

Last updated: Jan 08, 2024 11:15:20

It is possible to compute a new type of force that is an analogue to the shear force for warping (model type 6). The lateral-torsional moment is calculated in the design cross-sections of bars; for this moment, the diagrams along the length of the bars are generated for FE 7. This type of force is required in order to compute the tangential stresses in the analysis of the load-bearing capacity of elements subject to torsion.

Mosaic plot for the lateral-torsional moment Tw

## Nonlinear custom cross-sections

Last updated: Jan 08, 2024 11:15:20

Analysis of physically nonlinear bars for which a cross-section of arbitrary shape and components is generated in the "Cross-section Design Toolkit" module. Elements with such a cross-section can be physically nonlinear step-type, iterative with unloading with initial stiffness and iterative without unloading.

Custom cross-section for nonlinear analysis

## Accounting for orthotropy

Last updated: Jan 08, 2024 11:15:20

New check and limitation on the specified parameters for orthotropy stiffness. The stiffness should be positive:

• for plate FEs ν12 ≥ 0, ν21 ≥ 0, ν12*ν21 < 1;

• for solids ν12 ≥ 0, ν21 ≥ 0, ν13 ≥ 0, ν31 ≥ 0, ν23 ≥ 0, ν32 ≥ 0,

ν12*ν21 + ν23*(ν12*ν31 + ν32) + ν13*(ν21*ν32 + ν31) < 1

Conditions that the matrix of physical constants for orthotropy is positively definite:

• for plate FEs E1*E2 > (0.5*(E1*ν12+E2*ν21))^2;

• for solids

E1*E2*(1-ν23*ν32)*(1-ν13*ν31) > (0.5*(E1*(ν12+ν13*ν32)+E2*(ν21+ν31*ν23)))^2

E1*E3*(1-ν23*ν32)*(1-ν12*ν32) > (0.5*(E1*(ν13+ν12*ν23)+E3*(ν31+ν21*ν32)))^2

E2*E3*(1-ν13*ν31)*(1-ν12*ν32) > (0.5*(E2*(ν23+ν13*ν21)+E3*(ν32+ν12*ν31)))^2

## Analysis parameters

Last updated: Jan 08, 2024 11:15:20
• For the strain in FEs 55, 255, 265 and 295, an alternate sign rule is applied. The new rule states that strain along an axis of the element's local coordinate system has the sign "-" if nodes move in the direction of each other (compression), and the sign "+" if nodes move in the opposite direction (tension). If the projections of the nodes on this axis coincide, the sign of strain will depend on the order of node numbers defined for the element, that is, by the same order as previously defined.

Note:

Previously, strains were computed as the difference in displacements of the 2nd and 1st node. That is, the sign of strain depended on the order of node numbers defined for the element.

• In analysis of plate systems, for individual finite elements of shell, it is possible to define the sixth degree of freedom (rotation UZ relative to the axis orthogonal to the plane).

Account of the sixth DOF for the shell through the plate stiffness dialogue box

## Analysis of reactions

Last updated: Jan 08, 2024 11:15:20

Analysis of the load on fragment (reactions) and punching shear analysis for loads defined "by formula".